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Relative permeability assessment in a giant carbonate reservoir using

Digital Rock Physics

Zubair Kalam1, Samy Seraj1, Zahid Bhatti1,Alex Mock2, Pl Eric ren2, Vegar Ravlo2 and Olivier

Lopez21Abu Dhabi Company for Onshore Oil Operations (ADCO) and 2Numerical Rocks (Norway)

ABSTRACT

Representative relative permeability data are of great importance for accurate and more importantly

valid reservoir simulation models. Relative permeability tests are conventionally performed in

specialized laboratories through Special Core Analysis (SCAL) conducted on selected core plugs. Theexperiments can be time consuming and as such performed on a limited number of reservoir core plugs

to represent specific reservoir rock types (RRT), flow units and/or reservoir zones.

A detailed study to investigate the reliability and validity of water-oil relative permeability curves andend points were derived using the new discipline of Digital Rock Physics (DRP). Reservoir core plugs

from a giant carbonate reservoir in the Middle East on which imbibition water-oil relative permeabilitywere acquired were chosen for this huge validation study. The cores were selected and tested through acomprehensive SCAL program consisting of careful preserved core acquisition, selection/screening,

detailed characterization, testing and QC/QA of laboratory results using numerical simulation and

integration with multiple tests such as single-speed centrifuge and water-oil capillary pressure. The

DRP based investigations were performed as part of a blind study (relative permeability data unknownto DRP contractor) on 16 different RRT samples, comprising a vast range of lithofacies with core

porosities from 11 34% and permeabilities from micro-Darcy to several Darcies.

Relative permeabilities are quantified by adopting a multi-resolution integrated pore-scale modelingapproach based on X-ray computed tomography images and numerical 3D digital rock models. This

technique is able to capture the dominating pore classes present on the core plug scale: vuggy porosity,inter- and intragranular macro-porosity and micritic micro-porosity. Rock curves are generated for each

of the pore classes and then used in a steady-state upscaling routine to obtain primary drainage (water

saturation decreasing from 100% brine saturation) and imbibition (water saturation increasing) relative

permeability curves representing the entire core plug.

The comparisons between relative permeability curves derived from DRP and experimental steady state

tests provide an assessment on the validity of the DRP based tests. Comparisons have been performed

for each RRT and show an excellent match of laboratory measured relative permeability; typicallywithin 90% of the test results if rock-fluid wettability can be correctly postulated. Wettability variation

for different RRT and respective pore geometry can also be quantified, and thus significantly improve

the uncertainties in the predicted relative permeabilities.

INTRODUCTION

Conventionally, multiphase flow in porous media is described by means of the concept of relative

permeability functions. Accurate characterization of flow and fluid distribution is a key parameter for

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reservoir management. Relative permeability tests are traditionally performed in Special Core Analysis

(SCAL) laboratories and conducted on limited number of selected core plugs.

DRP studies have proven the capability to generate SCAL data at small scale mm to cm (Gomari et al.,

2011, Lopez et al., 2010, Kalam et al., 2010 and 2011, and Graderet al., 2010). In carbonate rocks,

pore structure is generally heterogeneous with pore size ranging from sub-micron to severalcentimeters. Thus, a large scatter of reservoir characterization properties is caused by these variations

in pore type, pore geometry and different porosity types. To predict multiphase flow properties of

carbonate reservoir rocks, it is necessary to characterize the different types of heterogeneity (i.e. rocktypes), to recognize which have important effects on fluid flow, and to capture them and the relevant

flow physics at different scales by up-scaling.

In this study performed over 9 months, DRP approach was applied on 100+ carbonate core plugs fromtwo giant carbonate reservoirs in the Middle East to numerically predict petrophysical properties and

water/oil relative permeability during imbibition from 3D rock models derived from X-ray micro

tomography imaging (MCT). Results of 18 selected core plugs comprising 6 different RRTs arepresented in this paper. These RRTs have both unimodal and multi-modal pore throat distributions

with permeabilities from 1 3000 mD and porosities from 15 35%.

METHODOLOGY

Laboratory test

Routine Core Analysis (RCA) has been conducted on the selected samples for this study to determineporosity and permeability. Laboratory measurements for water-oil relative permeability during first

imbibition were performed on selected core plugs from 6 different RRTs. Data reported in this study

were based on the steady state tests on composite cores (minimum of 3 plugs per RRT). The irreduciblewater saturation (Swi) was determined in each plug using the porous plate method with a maximum

capillary pressure of 7 bar. All experiments were conducted at reservoir temperature and reservoiroverburden pressure with insitu saturation monitoring using live oil and formation brine. Analyticaldata were history matched using the commercial software SENDRA.

Digital Rock Physics

Imaging, Modeling and Petrophysical Properties

All the samples investigated in this study were part of 1.5-inch diameter carbonate core plugs. They

were imaged with a Nanotom S nanofocus X-ray computed tomography system (MCT) at a resolution

of 19m per voxel. Microplug sub-samples were drilled from the core plug samples at selected

locations (rock typing) from end-cuts and scanned with the same scanner or where appropriate atthe European Synchrotron Radiation Facility in Grenoble, France (ESRF). Microplugs diameter is from

0.5mm to 10mm and resulting 3D images have resolutions between 0.28m and 5m per voxel.Microporous phase is often below the resolution of the CT scans. 3D models of the micorporous phase

are then constructed based on analysis of high resolution backscattered scanning electron microscope

(BSEM) images. Modeling and calculations of petrophysical properties are described by Lopez et al.

(SCA 2012), and are not detailed in this paper.

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Two-phase Flow Simulations

For microporous phase and intergranular porosity, simulations of multiphase flow are performed on anumerical pore network, which retains the essential features of the 3D rock models pore space (ren

et al., 1998). The multi-phase flow simulations are based on a quasi-static network model. In the

numerical simulations, flow is assumed to be laminar, capillary driven and fluids are immiscible (renet al., 1998). The wettability model used for the two-phase flow simulations is discussed in detail in

ren et al. (1998 and 2002). For vuggy porosity identified in core plug CT scans, flow properties aredirectly computed from CT scans using Lattice-Boltzman calculations (Ramstad et al. 2010).

Upscaling

Effective properties of the micro-/core plug samples are determined using steady state scale up

methods. The CT scan of the micro-/core plug is gridded according to the observed geometricaldistribution of the different rock types or porosity contributors. Each grid cell is then populated with

properties calculated on the pore scale images of the individual rock types. The following properties are

assigned to each grid cell; porosity, absolute permeability tensor (kxx, kyy, kzz), capillary pressure curveand relative permeability curve.

Single phase up-scaling is done by assuming steady state linear flow across the model. The single

phase pressure equations are set up assuming material balance and Darcys law:

facesotherat0nv

LxatPpxatPp

conditionsboundarywith0P)k

01

,0

(

The pressure equation is solved using a finite difference formulation. From the solution one can

calculate the average velocity and the effective permeability using Darcys law. By performing thecalculations in the three orthogonal directions, we can compute the effective or up-scaled permeability

tensor for the core sample.

Effective two-phase properties (i.e. capillary pressure and relative permeability) are calculated usingtwo-phase steady state up-scaling methods. We assume that the fluids inside the sample have come to

capillary equilibrium. This is a reasonable assumptions for small samples (

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RRT 6

RRT 6 is characterized by poorly sorted bioclastic floatstones with mud dominated facies andinterparticle, intraparticle and vuggy pore types. The measured Helium porosity of this rock type is in

the range of 26% and Klinkenberg corrected permeability of 10 to 25mD.

DRP and experimental porosity and permeability are close as shown in Table 1. Relative permeability

from DRP and steady state test are presented in Figure 1. Relative permeability from the 3reconstructed core plugs are quite close and match well the steady state test of RRT 6 as well as for the

reconstructed composite core. Swi from DRP are comparable to experimental value defined for the

composite core.

Table 1

Sample ID Lab CC.RRT6 DRP 1 - RRT6 DRP 2 - RRT6 DRP 3 - RRT6 DRP CC.RRT6

K(mD) 17.5 13.3 25.8 9.31 23.1

Porosity (frac.) 0.275 0.260 0.270 0.264 0.269

Swi 0.13 0.10 0.06 0.11 0.09

Sorw 0.19 0.18 (0.13*) 0.19 (0.09*) 0.20 (0.13*) 0.20

Krw(Sorw) 0.62 0.74 (0.88*) 0.56 (0.86*) 0.63 (0.82*) 0.70

* Pc=-7bar

RRT7

Mostly homogeneous moderately sorted bioclastic grainstones / rudstones are represented in RRT7.

Porosity occurs dominantly as intraparticle and interparticle. These carbonates are characterized by

porosity around 28% and permeabilities of 100-250mD.Computed and experimental porosity are very similar (~28%) while permeability from DRP is slightly

lower but comparable within a reasonable range (Table2). Relative permeability from the 3

reconstructed samples and the synthetic composite core are matching very well steady state floodingtest results (Figure 2). Swi from DRP and experiment are the same (9-10%).

Table 2

Sample ID Lab CC.RRT7 DRP 1 - RRT7 DRP 2 - RRT7 DRP 3 - RRT7 DRP- CC.RRT7

k(mD) 191.6 95.6 108.1 98.0 103.3

Porosity (frac.) 0.278 0.271 0.284 0.287 0.276

Swi 0.09 0.09 0.1 0.1 0.09

Sorw 0.32 0.30 (0.13*) 0.29 (0.13*) 0.32 (0.15*) 0.30

krw(Sorw) 0.75 0.62 (0.82*) 0.67 (0.88*) 0.64 (0.86*) 0.63

* Pc=-7bar

RRT8a

RRT8a is characterized by a well cemented bioclastic grainstone with mostly vuggy porosity. Observed

porosity of this carbonate is about 13% and permeability in the 1-3D range.

Both porosity and permeability are well captured with DRP (Table3). Steady state tests conducted onRRT8a sample show a difficulty to reconcile raw and history match (HM) data. Raw experimental data

were then fitted using Corey parameterization on most trustable experimental as shown in Figure 3. Oil

relative permeability from DRP, steady state flooding test and Corey fitting on experimental (lab) dataare showing very good agreement. While water relative permeability from tests shows a suspicious low

value at low water saturation (Sw lower than 40%). These values have been ignored during Corey

fitting. DRP and Corey fitted water relative permeability show a very good agreement.

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Table 3

Sample ID Lab CC.RRT8a DRP 1 - RRT8a DRP 2 - RRT8a DRP 3 - RRT8a DRP CC.RRT8a

k(mD) 1672 1326 2533 1490 2097

Porosity (frac.) 0.130 0.135 0.110 0.134 0.131

Swi 0.164 0.13 0.14 0.14 0.13

Sorw 0.28 0.25 (0.11*) 0.24 (0.11*) 0.26 (0.11*) 0.25 (0.11*)

krw(Sorw) 0.79 0.80 (0.87*) 0.80 (0.88*) 0.83 (0.87*) 0.82 (0.88*)

* Pc=-7bar

RRT8b

Bioclastic grainstones/rudstones with a high degree of recrystallization has been observed in RRT8b.

The porosity of these carbonates vary between 27-30% and the dominant pore type are vuggy and

intraparticle. Permeabilities range between 200-700mD.Porosity form the 3 reconstructed core plugs and the composite core plug are within the same range

(27-30%) and the permeability of the 3 reconstructed core plugs show a significant spread from 192.4

to 653.4mD (Table 4). The synthetic composite core has a average permeability of 379.6mD andporosity of 29%. Relative permeability of the 3 DRP samples and the synthetic composite core are

matching well the steady state test results (Figure 4).

Table 4

Sample ID Lab - CC.RRT8b DRP 1 - RRT8b DRP 2 - RRT8b DRP 3 - RRT8b DRP CC.RRT8b

k(mD) 257.7 302.4 653.6 192.4 379.6

Porosity (frac.) 0.266 0.296 0.278 0.272 0.290

Swi 0.078 0.11 0.07 0.14 0.09

Sorw 0.30 0.25 (0.12*) 0.29 (0.13*) 0.25 (0.15*) 0.29

krw(Sorw) 0.75 0.73 (0.81*) 0.76 (0.82*) 0.74 (0.81*) 0.73

* Pc=-7bar

RRT11

RRT11 is characterized by bioclastic wackestones to packstones with a high percentage of micritizedcomponents. Dominant pore types are intraparticle, interparticle and vuggy. The observed porosities

are around 32% and the permeability is in the 10-30mD range.

Porosity from DRP and experiment are close and permeability of the 3 reconstructed samples is

ranging from 7.07 to 40.2mD compared to 11.4mD for experimental value (Table 5). The syntheticcomposite core plug has a permeability of 14.0mD and porosity of 32% very close to the experimental

composite core. Swi of the composite core is unexpectedly high at 0.177 (probably due to weighting

from 2 additional plugs, not used in DRP tests) compared to individual measured value of each of theDRP core plugs of 0.06 - 0.08, respectively. Therefore, to better compare the data sets, simulated and

experimental relative permeability have been reported as a function normalized water saturation with

respect to initial water saturations as:

wi

wiwwN

S

SSS

1(1)

Relative permeability from the 3 reconstructed core plugs show a significant spread but capture well

the results from the steady state test (Figure 5). Only experimental oil relative permeability close toresidual oil saturation is slightly greater to the DRP ones but end point value is very similar (~11%)

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Table 5

Sample ID Lab - CC.RRT11 DRP 1 - RRT11 DRP 2 - RRT11 DRP 3 - RRT11 DRP CC.RRT11

k(mD) 11.4 17.3 40.2 7.07 14.0

Porosity (frac.) 0.316 0.331 0.347 0.308 0.320

Swi 0.177 0.06 0.08 0.07 0.07

Sorw 0.11 0.16 (0.12*) 0.13 (0.08*) 0.13 (0.11*) 0.17 (0.12*)

krw(Sorw) 0.74 0.81 (0.89*) 0.87 (0.94*) 0.76 (0.88*) 0.85 (0.92*)

* Pc=-7bar

RRT15

Bioclastic wackestones to packstones are characterizing RRT15. Micritization of the components has

been observed. Dominant pore types are vuggy, interparticle and intraparticle. Porosities around 33%and permeabilities of 30-70mD are typical.

The 3 samples from RRT15 exhibit significant variations for both permeability and porosity as shown

in Table 6. Porosity of the 3 reconstructed samples varies from 27.1 to 37.2% and the experimentalvalue for the composite core is 31.0%. Permeability is ranging from 27.2 to 52.2mD for an

experimental value of 35.6mD. Figure 6 shows the comparison of the 3 DRP relative permeability and

the steady state test ones. The 3 DRP relative permeability are significantly different and cannot becompared directly to results from the composite core. Porosity and permeability of the synthetic

composite core are well in line with the experimental data. Relative permeability from DRP and steady

state test has been compared in Figure 6. Oil relative permeability is matching well the laboratory test.

Water relative permeability from DRP is slightly lower than experimental one but within the range ofuncertainties for this kind of experiment.

Table 6

Samlple ID Lab - CC.RRT15 DRP1 - RRT15 DRP2 - RRT15 DRP3 - RRT15 DRP - CC.RRT15

k(mD) 35.6 52.2 42.6 27.2 40.8

Porosity (frac.) 0.310 0.271 0.338 0.372 0.332

Swi 0.11 0.08 0.08 0.08 0.08

Sorw 0.17 0.18 (0.14*) 0.20 (0.15*) 0.16 (0.13*) 0.15

krw(Sorw) 0.70 0.60 (0.66*) 0.63 (0.70*) 0.83 (0.89*) 0.68

* Pc=-7bar

CONCLUSIONS

The DRP multi-scale approach used in this study yields reliable and consistent SCAL data forheterogeneous carbonate rocks under oil-wet conditions. The study was conducted without any

knowledge of experimental results (blind study). Only fluid properties (density, viscosity and

interfacial tension) and wettability preferences were provided to the DRP contractor. The comparisonsbetween relative permeability curves derived from DRP and experimental steady state tests have shown

an excellent match for the investigated RRTs.The results presented in this paper show that DRP approach can be used to provide fast, high quality

SCAL data at a scale where experiments are commonly conducted in SCAL laboratories. SCAL datafrom DRP were calculated on both single and composite core plugs.

ACKNOWLEDGEMENT

The authors wish to acknowledge ADCO and ADNOC Management for approval in submitting this

paper. ADCO DRP team members are duly acknowledged for their participation and whole hearted

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cooperation in providing the reservoir core samples, and interesting contributions during the many

technical discussions.

REFERENCES

Lopez, O., Mock, A., ren, P. E., Long, H., Kalam, M. Z., Vahrenkemp, V., Gibrata, M., Seraj, S.,Chacko, S., Al Hosni, H. and Vizamora, A., 2012, Validation of fundamental carbonate reservoir core

properties using Digital Rock Physics, SCA2012-19, Aberdeen.

Gomari, K. A. R., Berg, C. F., Mock, A., ren, P.-E., Petersen, E. B. Jr., Rustad, A. B., Lopez, O.,

2011, Electrical and petrophysical properties of siliciclastic reservoir rocks from pore-scale modeling,paper SCA2011-20 presented at the 2011 SCA International Symposium, Austin, Texas.

Grader, A., Kalam, M. Z., Toelke, J., Mu, Y., Derzhi, N., Baldwin, C., Armbruster, M., Al Dayyani, T.,

Clark, A., Al Yafei, G. B. And Stenger, B., 2010, A comparative study of DRP and laboratory SCALevaluations of carbonate cores, paper SCA2010-24 presented at the 2010 SCA International

Symposium, Halifax, Canada.

Lopez, O., Mock, A., Skretting, J., Petersen, E.B.Jr, ren, P.E. and Rustad, A.B., 2010, Investigation

into the reliability of predictive pore-scale modeling for siliciclastic reservoir rocks, paper SCA2010-41

presented at the 2010 SCA International Symposium, Halifax, Canada.

Kalam, M. Z., Al Dayyani, T., Clark, A., Roth, S., Nardi, C., Lopez, O. and ren, P. E., 2010, Case

study in validating capillary pressure, relative permeability and resistivity index of carbonates from X-

Ray micro-tomography images, paper SCA2010-02 presented at the 2010 SCA InternationalSymposium, Halifax, Canada.

Kalam, M.Z., Al Dayyani, T., Grader, A., and Sisk, C., 2011, Digital rock physics analysis in complex

carbonates, World Oil, May 2011.

Ramstad, T., ren, P. E., and Bakke, S., 2010, Simulations of two phase flow in reservoir rocks using a

Lattice Boltzmann method, SPE J., SPE 124617.

ren, P.E. and Bakke, S., Process Based Reconstruction of Sandstones and Prediction of Transport

Properties, Transport in Porous Media, 2002, 46, 311-343

ren, P.E, Antonsen, F., Ruesltten, H.G., and Bakke, S., 2002, Numerical simulations of NMR

responses for improved interpretation of NMR measurements in rocks, SPE paper 77398, presented atthe SPE Annual Technical Conference and Exhibition, San Antonio, Texas.

ren, P. E., Bakke, S. and Arntzen, O. J., 1998, Extending predictive capabilities to network models,SPE J., 3, 324336.

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Figures

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Relativepermeability

DRP 1 - RRT6DRP 2 - RRT6

DRP 3 - RRT6Lab - CC.RRT6HM - Lab - CC.RRT6

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Figure 1: DRP and steady state test Relative permeability for RRT 6

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Figure 3: DRP and steady state test Relative permeability for RRT 8a

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Figure 4: DRP and steady state test Relative permeability for RRT 8b

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